考虑分形效应的煤岩损伤模型及渗透率模型
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摘要
为探索煤岩失稳破坏过程中损伤演化和渗透率演化规律,用分形维数表征损伤演化,研究煤岩损伤破坏过程中渗透特性。基于孔裂隙的体积分形维数与应力关系,推导出分形维数表征的Weibull分布参数,利用煤岩孔裂隙的分形维数和孔隙率的关系,求解煤岩裂隙随有效应力的变化量γ;根据Mohr-Coulomb准则和Poiseuille定律,分别构建考虑分形效应的煤岩损伤本构模型和煤岩渗透率模型,分析损伤和渗透率的联动关系。结果表明:峰值应力前,孔裂隙体积分形维数与轴向应力和应变均成线性关系;随着有效应力的增大,煤岩孔隙率增大,煤岩渗透率先平缓增大后急剧增大;同一应力点下的渗透率随ln(1/r)的增大而增大;所建立的煤岩损伤本构模型和渗透率模型,与试验结果均有较高的吻合度。
In order to investigate the law of damage evolution and permeability evolution of coal during unstable failure process,relationships between volume fractal dimension of pore-fracture networks and stress and strain were introduced respectively. According to the relationship between volume fractal dimension of pore-fracture and stress,Weibull distribution parameters characterized by fractal dimension characteristics were derived. According to the relationship between the fractal dimension and porosity of pore-fracture of coal,variation( γ) of coal fractures with effective stress was solved. Based on Mohr-Coulomb criterion and Poiseuille law, a coal damage constitutive model and a permeability model considering the fractal effect were built. Then the relationship between damage and permeability was analyzed. The results show that before peak stress,the volume fractal dimension of pore-fracture is linear with axial stress and strain,that porosity of coal increases with the increases of effective stress,and the permeability increases first slowly and then sharply,that the permeability increases with the increase of ln( 1/r) at the same stress point,and that solutions of both the damage constitutive model and the permeability model of coal conform closely with the experimental data.
In order to investigate the law of damage evolution and permeability evolution of coal during unstable failure process,relationships between volume fractal dimension of pore-fracture networks and stress and strain were introduced respectively. According to the relationship between volume fractal dimension of pore-fracture and stress,Weibull distribution parameters characterized by fractal dimension characteristics were derived. According to the relationship between the fractal dimension and porosity of pore-fracture of coal,variation( γ) of coal fractures with effective stress was solved. Based on Mohr-Coulomb criterion and Poiseuille law, a coal damage constitutive model and a permeability model considering the fractal effect were built. Then the relationship between damage and permeability was analyzed. The results show that before peak stress,the volume fractal dimension of pore-fracture is linear with axial stress and strain,that porosity of coal increases with the increases of effective stress,and the permeability increases first slowly and then sharply,that the permeability increases with the increase of ln( 1/r) at the same stress point,and that solutions of both the damage constitutive model and the permeability model of coal conform closely with the experimental data.
引文
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[2]谢和平.脆性材料中的分形损伤[J].机械强度,1995,17(2):75-82.XIE Heping.Fractal damage in brittle materials[J].Journal of Mechanical Strength,1995,17(2):75-82.
[3]陈新,吕文涛,孙靖亚.基于图像分析的节理岩体单轴压缩损伤演化研究[J].岩石力学与工程学报,2014,33(6):1 149-1 157.CHEN Xin,LYU Wentao,SUN Jingya.Damage evolution of jointed rock masses under uniaxial compression based on digital image analysis[J].Chinese Journal of Rock Mechanics and Engineering,2014,33(6):1 149-1 157.
[4]惠鑫,马凤山,徐嘉谟,等.考虑节理裂隙尺寸与方位分布的岩石统计损伤本构模型研究[J].岩石力学与工程学报,2017,36(增1):3 233-3 238.HUI Xin,MA Fengshan,XU Jiamo,et al.Study on statistical damage constitutive model for rocks considering length and occurrence distribution of joint fissures[J].Chinese Journal of Rock Mechanics and Engineering,2017,36(S1):3 233-3 238.
[5]薛东杰,周宏伟,邓淋升,等.低渗煤岩气液两相流分形运动方程[J].工程科学与技术,2018,50(4):30-40.XUE Dongjie,ZHOU Hongwei,DENG Linsheng,et al.Fractal dynamics of gas-liquid flow in low-permeability coal[J].Advanced Engineering Sciences,2018,50(4):30-40.
[6]YU Boming,CHENG Ping.A fractal permeability model for bi-dispersed porous media[J].International Journal of Heat and Mass Transfer,2002,45(14):2 983-2 993.
[7]LEMAITRE J.How to use damage mechanics[J].Nuclear Engineering and Design,1984,80(3):233-245.
[8]梁冰,王维华,李宏艳,等.基于损伤变量的煤柱合理留设试验研究[J].安全与环境学报,2013,13(5):179-182.LIANG Bing,WANG Weihua,LI Hongyan,et al.Experiment study on the regularity of the coal pillar residua based on the damage variables[J].Journal of Journal of Safety and Environment,2013,13(5):179-182.
[9]吴二林,魏厚振,颜荣涛,等.考虑损伤的含天然气水合物沉积物本构模型[J].岩石力学与工程学报,2012,31(增1):3 045-3 050.WU Erlin,WEI Houzhen,YAN Rongtao,et al.Constitutive model for gas hydrate-brearing sediments considering damage[J].Chinese Journal of Rock Mechanics and Engineering,2012,31(S1):3 045-3 050.
[10]曹文贵,张升.基于Mohr-Coulomb准则的岩石损伤统计分析方法研究[J].湖南大学学报:自然科学版,2005,32(1):43-47.CAO Wengui,ZHANG Sheng.Study on the statistical analysis of rock damage based on Mohr-Coulomb criterion[J].Journal of Hunan University:Natural Sciences,2005,32(1):43-47.
[11]NOLEN-HOEKSEMA R C,GORDON R B.Optical detection of crack patterns in the opening-mode fracture of marble[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1987,24(2):135-144.
[12]冯春,李志刚,李世海.脆性土石混合体单轴压缩特性的影响因素研究[J].计算力学学报,2018,35(3):356-363.FENG Chun,LI Zhigang,LI Shihai.Study on uniaxial compression characteristics of brittle rock and soil aggregate[J].Chinese Journal of Computational Mechanics,2018,35(3):356-363.
[13]ZHOU Hongwei,ZHONG Jiangcheng,REN Weiguang,et al.Characterization of pore-fracture networks and their evolution at various measurement scales in coal samples using X-rayμCT and a fractal method[J].International Journal of Coal Geology,2018,189:35-49.
[14]CHEN Dong,PAN Zhejun,SHI Jiquan,et al.A novel approach for modelling coal permeability during transition from elastic to post-failure state using a modified logistic growth function[J].International Journal of Coal Geology,2016,163:132-139.
[15]LI Wei,ZHAO Huan,LI Siqi,et al.A fractal model of effective stress of porous media and the analysis of influence factors[J].Results in Physics,2018,8:920-925.